Why are the larger dragon-flies usually called horse-stingers?

Because they are supposed to have a propensity to sting horses, and (it may be presumed) any other animal which may irritate them. But, not one of the tribe is furnished with a sting. They have, however, a pair of most formidable looking jaws, though even these are not strong enough to inflict injury upon any of the larger animals, and are only employed to crush a fly, or to wing a moth or a butterfly.

We may here mention that the larvae of the dragonfly are provided with an apparatus probably unmatched in the insect world. This consists of a mask, or the under lip of the larva, which conceals the mouth and face, and two plates covering the jaws. While this strange organ is at rest, it applies close to and covers the face. When the insects would use it, they unfold it like an arm, catch their prey by means of the plates, which are toothed like jaws, and then partly refold the lip, so as to hold the prey to the mouth. De Geer observes, the larvae of the dragon-fly do not, however, trust to this mask alone, for surprising their prey, but steal upon it, as a cat does upon a bird, very slowly, and as if they counted their steps; and then, by suddenly unmasking, seize it by surprise: so artful are they, that insects, and even small fishes, find it difficult to elude their attacks.

Why do the larvae of dragon-flies suck in and eject water to aid their progress in swimming?

Because the jet propels the creature through the water, in consequence of its being resisted by the stationary mass of the fluid behind it, and a contrary current being thence produced by this singular pumping. As the insect, between every stroke of the internal piston, is obliged to draw in a fresh supply of water, an interval consequently occurs between the strokes, during which it will sometimes elevate its tail above water, and squirt out a small stream like that from a little syringe. Among other purposes of this wonderful apparatus are its aid in bringing small water insects within its reach, and its share in respiration, in which it somewhat resembles the gills of fish.